Topological Quantum Field Theory and Four-Manifolds
I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit results for the Donaldson invariants of non-simply connected manifolds, and for generalizations of these invariants to the gauge groupSU(N);(b) compactifications to lower dimensions, and connections to three-manifold topology and to intersection theory on the moduli space of flat connections on Riemann surfaces; (c) four-dimensional theories with critical behaviour, which give some remarkable constraints on Seiberg-Witten invariants and new results on the geography of four-manifolds.
KeywordsModulus Space Gauge Group Intersection Pairing Modular Form Supersymmetric Gauge Theory
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